Question

If the pattern below is continued, find the 10th fraction in this sequence: 1/2+1/6+1/12+1/20+1/30.....=
1.1/60
2.1/90
3.1/100

Answer 1

$Solution:\\\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...\\If\ you\ write\ it \;like\;this\ and\ continue:\\\frac{1}{2}+\frac{1}{2\times3}+\frac{1}{2\times(3+3)}+\frac{1}{2\times(3+3+4)}+\\+\frac{1}{2\times(3+3+4+5)}+\frac{1}{2\times(3+3+4+5+6)}+\\+\frac{1}{2\times(3+3+4+5+6+7)}+\frac{1}{2\times(3+3+4+5+6+7+8)}+\\+\frac{1}{2\times(3+3+4+5+6+7+8+9)}+\\+\frac{1}{2\times(3+3+4+5+6+7+8+9+10)}+...\\This\ is\ the \;tenth \;fraction\ of\ the\ sequence\\\frac{1}{2\times(3+3+4+5+6+7+8+9+10)}=\frac{1}{110}.\\Answer:the\ 10th\ fraction\;is\;\frac{1}{110}$